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For the analysis of square contingency tables with ordered categories, Tomizawa (1991) considered
the diagonal uniform association symmetry (DUS) model, which has a multiplicative form for cell probabilities
and has the structure of uniform association in the tables constructed using two diagonals that are equidistant
from the main diagonal. This paper proposes another DUS model which has a similar multiplicative form
for cumulative probabilities. The model indicates that the odds that an observation will fall in row category
i or below and column category i+k or above, instead of in column category i or below and row category
i+k or above, increase (decrease) exponentially as the cutpoint i increases for a fixed k. Examples
are given. 相似文献
13.
Sadao Tomizawa 《Journal of applied statistics》1992,19(4):509-512
For the analysis of square contingency tables with ordered categories, this paper introduces a simple symmetry model in which the expected frequency has an exponential form along every subdiagonal of the table. The model is applied to the data on unaided distance vision of 3168 pupils at elementary schools in Tokyo which were reported earlier by Tomizawa, and a result of interest is obtained. 相似文献
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For square contingency tables with ordered categories, this paper proposes a measure to represent the degree of departure from the marginal homogeneity model. It is expressed as the weighted sum of the power-divergence or Patil–Taillie diversity index, and is a function of marginal log odds ratios. The measure represents the degree of departure from the equality of the log odds that the row variable is i or below instead of i+1 or above and the log odds that the column variable is i or below instead of i+1 or above for every i. The measure is also extended to multi-way tables. Examples are given. 相似文献
15.
For square contingency tables with ordered category, the present paper proposes the double linear diagonals-parameter symmetry
(D-LDPS) model which implies the structure of both asymmetry with respect to the main diagonal and with respect to the reverse
diagonal in the table. The D-LDPS model may be appropriate for a square ordinal table if it is reasonable to assume an underlying
bivariate normal distribution with equal marginal variances. The present paper also gives the orthogonal decomposition of
the double symmetry model into the D-LDPS model and the double marginal mean equality model. An example is given. 相似文献
16.
This paper proposes a model, which is an extension-of-symmetry model, for square contingency tables with the same nominal row and column classifications. The model states that the absolute values of difference between the conditional probability that an observation will fall in cell (i, j) on condition that it falls in cell (i, j) or (j, i) and the conditional probability that it falls in cell (j, i) on the same condition, are constant for every i≠j. The model describes a structure of asymmetry (not symmetry), and it is applied to the data on a nominal scale. An example is given. 相似文献
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Sadao Tomizawa 《统计学通讯:理论与方法》2013,42(2):477-488
For square contingency tables rith ordered categories, this paper proposes two kinds of extensions of marginal homogeneity model and gives decompositions for the Liseer diagonals-parameter symmetry model considered by Agresti (1983a) using the proposed models- The proposed models are also applied to an unaided vision data. 相似文献
18.
Sadao Tomizawa Takashi Seo Hideharu Yamamoto 《Journal of applied statistics》1998,25(3):387-398
For square contingency tables that have nominal categories, Tomizawa considered two kinds of measure to represent the degree of departure from symmetry. This paper proposes a generalization of those measures. The proposed measure is expressed by using the average of the power divergence of Cressie and Read, or the average of the diversity index of Patil and Taillie. Special cases of the proposed measure include Tomizawa's measures. The proposed measure would be useful for comparing the degree of departure from symmetry in several tables. 相似文献
19.
For square contingency tables with ordered categories, the conditional symmetry model is decomposed into the palindromic symmetry and the modified marginal homogeneity models, and moreover into the generalized palindromic symmetry model and two other models. The data on unaided vision first analysed by Stuart (1953, 1955) is analysed again by using the decompositions. 相似文献